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1. Energy Harvesting Performance of Thick Oscillating Airfoils Using a Discrete Vortex Model

   https://doi.org/10.1115/1.4056339  

   Kamrani Fard, Kiana; Ngo, Vickie; Pence, Deborah; Liburdy, Jim A. (November 2022, Journal of Fluids Engineering)

   Abstract The energy harvesting performance of thick oscillating airfoils is predicted using an inviscid discrete vortex model (DVM). NACA airfoils with different leading-edge geometries are modeled that undergo sinusoidal heaving and pitching with reduced frequencies, k = f c/U∞, in the range 0.06–0.14, where f is the heaving frequency of the foil, c the chord length, and U the freestream velocity. The airfoil pitches about the mid-chord with heaving and pitching amplitudes of h0 = 0.5c and θ0 = 70°, respectively, known to be in the range of peak energy harvesting efficiencies. A vortex shedding initiation criteria is proposed based on the transient local wall stress distribution determined from computational fluid dynamics (CFD) simulations and incorporates both timing and location of leading-edge separation. The scaled shedding times are shown to be predicted over the range of reduced frequencies using a timescale based on the leading-edge shear velocity and radius of curvature. The convection velocity of the shed vortices is also modeled based on the reduced frequency to better capture the dynamics of the leading-edge vortex. An empirical trailing-edge separation correction is applied to the transient force results using the effective angle of attack modified to include the pitching component. Impulse theory is applied to the DVM to calculate the transient lift force and compares well with the CFD simulations. Results show that the power output increases with increasing airfoil thickness and is most notable at higher reduced frequencies where the power output efficiency is highest. 

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2. On the noise generation and unsteady performance of combined heaving and pitching foils

   https://doi.org/10.1088/1748-3190/acd59d  

   Wagenhoffer, Nathan; Moored, Keith W.; Jaworski, Justin (May 2023, Bioinspiration & Biomimetics)

   Abstract A transient two-dimensional acoustic boundary element solver is coupled to a potential flow boundary element solver via Powell's acoustic analogy to determine the acoustic emission of isolated hydrofoils performing biologically-inspired motions. The flow-acoustic boundary element framework is validated against experimental and asymptotic solutions for the noise produced by canonical vortex-body interactions. The numerical framework then characterizes the noise production of an oscillating foil, which is a simple representation of a fish caudal fin. A rigid NACA 0012 hydrofoil is subjected to combined heaving and pitching motions for Strouhal numbers ($0.03 < St < 1$) based on peak-to-peak amplitudes and chord-based reduced frequencies ($0.125 < f^* < 1$) that span the parameter space of many swimming fish species. A dipolar acoustic directivity is found for all motions, frequencies, and amplitudes considered, and the peak noise level increases with both the reduced frequency and the Strouhal number. A combined heaving and pitching motion produces less noise than either a purely pitching or purely heaving foil at a fixed reduced frequency and amplitude of motion. Correlations of the lift and power coefficients with the peak root-mean-square acoustic pressure levels are determined, which could be utilized to develop long-range, quiet swimmers. 

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3. Experimental Study of Inertia-based passive Deformation of a Heaving and Pitching Airfoil Operating in the Energy Harvesting Regime

   Siala, F.F.; Fard, K.; Liburdy, J.A. (October 2019, Physics of fluids)

   The effects of passive, inertia-induced surface deformation at the leading and trailing edges of an oscillating airfoil energy harvester are investigated experimentally at reduced frequencies of k = f c=U¥ = 0.10, 0.14 and 0.18. Wind tunnel experiments are conducted using phase-resolved, two-component particle image velocimetry to understand the underlying flow physics, as well as to obtain force and pitching moment estimates using the vortex-impulse theory. Results are obtained for leading and trailing edge deformation separately. It is shown that both forms of deformation may alter the leading edge vortex inception and detachment time scales, as well as the growth rate of the circulation. In addition, surface deformation may also trigger the generation of secondary vortical structures, and suppress the formation of trailing edge vortices. The total energy harvesting efficiency is decomposed into contributions of heaving and pitching motions. Relative to the rigid airfoil, the deforming leading and trailing edge segments are shown to increase the energy harvesting efficiency by approximately 17% and 25%, respectively. However, both the deforming leading and trailing edge airfoils operate most efficiently at k = 0:18, whereas the peak efficiency of the rigid airfoil occurs at k = 0:14. It is shown that the deforming leading and trailing edge airfoils enhance the heaving contribution to the total efficiency at k = 0:18 and the negative contribution of the pitching motion at high reduced frequencies can be alleviated by using a deforming trailing edge. 

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4. Power Estimation of Flapping Foil Energy Harvesters Using Vortex Impulse Theory

   Siala, F.F.; Liburdy, J.A. (October 2019, Renewable energy)

   This study explores the feasibility of using the vortex impulse approach, based on experimen- tally generated velocity elds to estimate the energy harvesting performance of a sinusoidally apping foil. Phase-resolved, two-component particle image velocimetry measurements are conducted in a low-speed wind tunnel to capture the ow eld surrounding the apping foil at reduced frequencies of k = fc=U1 = 0.06 - 0.16, pitching amplitude of 0 = 70 and heaving amplitude of h0=c = 0:6. The model results show that for the conditions tested, a maximum energy harvesting eciency of 25% is attained near k = 0:14, agreeing very well with published numerical and experimental results in both accuracy and general trend. The vortex impulse method identi es key contributions to the transient power production from both linear and angular momentum eects. The eciency reduction at larger values of reduced frequencies is shown to be a result of the reduced power output from the angular momentum. Further, the impulse formulation is decomposed into contributions from posi- tive and negative vorticity in the ow and is used to better understand the uid dynamic mechanisms responsible for producing a peak in energy harvesting performance at k = 0:14. At the larger k values, there is a reduction of the advective time scales of the leading edge vortex (LEV) formation. Consequently, the LEV that is shed during the previous half cycle interacts with the foil at the current half cycle resulting in a large negative pitching power due to the reversed direction of the kinematic motion. This vortex capture process signif- icantly decreases the total cycle averaged power output and energy harvesting eciency. These results show the link between the kinematic motion and LEV time scales that aect the overall power production. 

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5. Experimental Investigation of the Unsteady Aerodynamics of Oscillating Airfoils in the Energy Harvesting Regime

   Siala, F.F (July 2019, Dissertation)

   The rising global trend to reduce dependence on fossil fuels has provided significant motivation toward the development of alternative energy conversion methods and new technologies to improve their efficiency. Recently, oscillating energy harvesters have shown promise as highly efficient and scalable turbines, which can be implemented in areas where traditional energy extraction and conversion are either unfeasible or cost prohibitive. Although such devices are quickly gaining popularity, there remain a number of hurdles in the understanding of their underlying fluid dynamics phenomena. The ability to achieve high efficiency power output from oscillating airfoil energy harvesters requires exploitation of the complexities of the event of dynamic stall. During dynamic stall, the oncoming flow separates at the leading edge of the airfoil to form leading ledge vortex (LEV) structures. While it is well known that LEVs play a significant role in aerodynamic force generation in unsteady animal flight (e.g. insects and birds), there is still a need to further understand their spatiotemporal evolution in order to design more effective energy harvesting enhancement mechanisms. In this work, we conduct extensive experimental investigations to shed-light on the flow physics of a heaving and pitching airfoil energy harvester operating at reduced frequencies of k = fc=U1 = 0.06-0.18, pitching amplitude of 0 = 75 and heaving amplitude of h0 = 0:6c. The experimental work involves the use of two-component particle image velocimetry (PIV) measurements conducted in a wind tunnel facility at Oregon State University. Velocity fields obtained from the PIV measurements are analyzed qualitatively and quantitatively to provide a description of the dynamics of LEVs and other flow structures that may be present during dynamic stall. Due to the difficulties of accurately measuring aerodynamic forces in highly unsteady flows in wind tunnels, a reduced-order model based on the vortex-impulse theory is proposed for estimating the aerodynamic loadings and power output using flow field data. The reduced-order model is shown to be dominated by two terms that have a clear physical interpretation: (i) the time rate of change of the impulse of vortical structures and (ii) the Kutta-Joukowski force which indirectly represents the history effect of vortex shedding in the far wake. Furthermore, the effects of a bio-inspired flow control mechanism based on deforming airfoil surfaces on the flow dynamics and energy harvesting performance are investigated. The results show that the aerodynamic loadings, and hence power output, are highly dependent on the formation, growth rate, trajectory and detachment of the LEV. It is shown that the energy harvesting efficiency increases with increasing reduced frequency, peaking at 25% when k = 0.14, agreeing very well with published numerical results. At this optimal reduced frequency, the time scales of the LEV evolution and airfoil kinematics are matched, resulting in highly correlated aerodynamic load generation and airfoil motion. When operating at k > 0:14, it is shown that the aerodynamic moment and airfoil pitching motion become negatively correlated and as a result, the energy harvesting performance is deteriorated. Furthermore, by using a deforming airfoil surface at the leading and trailing edges, the peak energy harvesting efficiency is shown to increase by approximately 17% and 25% relative to the rigid airfoil, respectively. The performance enhancement is associated with enhanced aerodynamic forces for both the deforming leading and trailing edges. In addition, The deforming trailing edge airfoil is shown to enhance the correlation between the aerodynamic moment and pitching motion at higher reduced frequencies, resulting in a peak efficiency at k = 0:18 as opposed to k = 0:14 for the rigid airfoil. 

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